Summary
This report was conceived as a source for the relations between five pneumatic parameters of carrier gas — inlet and outlet pressure, inlet and outlet velocity, and average velocity. Any pair of these parameters can be independent while the remaining three can be expressed as functions of the independent pair. As the total number of the independent pairs is ten, thirty different functions describing relations between arbitrary independent pairs and dependent parameters can be identified. All thirty were derived below together with the complete set of bounds for variations of independent parameters. To derive some relations, a third order rational equation had to be solved. Some properties of that solution are discussed. A simple case of vacuum operations with zero outlet pressure has also been considered.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- dc :
-
column diameter length
- F(·):
-
function, Eq. (49) 1
- f(·):
-
function, Eq. (33) 1
- G(·):
-
function, Eq. (77) 1
- g(·):
-
function, Eq. (34) 1
- j(·):
-
function, Eq. (29) 1
- L :
-
column length length
- P :
-
p i/p o 1
- p :
-
pressure mass/length/time2
- pav(·):
-
function, Eqs. (56), (62) 1
- Q :
-
p o/p i 1
- R(·):
-
function, Eq. (74) 1
- r :
-
pneumatic resistance mass/length2/time
- s :
-
arbitrary variable 1
- t M :
-
hold-up time time
- u :
-
carriere gas velocity length/time
- ū :
-
averageu length/time
- x :
-
distance from inlet length
- γ:
-
column permiability length3time/mass
- η:
-
fluid viscosity mass/length/time
References
J. J. Van Deemter, F. J. Zuiderweg, A. Klinkenberg, Chem. Eng. Sci.5, 271 (1956).
M. J. E. Golay, in “Gas Chromatography”, D. H. Desty, ed., Academic Press, London, 1958, p. 36–55.
G. H. Stewart, S. L. Seager, J. C. Giddings, Anal. Chem.31 (10), 1738 (1959).
J. C. Giddings, L. Seager, G. H. Stewart, Anal. Chem.32 (7), 867 (1960).
D. F. Ingraham, C. F. Shoemaker, W. Jennings, J. HRC5 (5), 227 (1982).
W. Jennings, “Analytical gas chromatography”, Academic Press, Orlando, Florida, 1987.
G. Guiochon., C. L. Guillemin, “Quantitative gas chromatography for laboratory analysis and on-line control,” Elsevier, Amsterdam, 1988.
J. C. Giddings, “Unified separation science,” John Wiley & Sons, New York, 1991.
Wolfram Research Inc., “Mathematica”, version 2.2 edition, Wolfram Research, Champaign, IL, 1992.
G. Guiochon, in “Chromatographic Review”, M. Lederer, ed., vol. 8, Elsevier, Amsterdam, 1966, p. 1–47.
A. T. James, J. P. Martin, Biochem. J.50, 679 (1952).
M. Q. Thompson, in “Electronic Pressure Control in Gas Chromatography”, S. S. Stafford, ed., Hewlett-Packard Co., Part Number 5182-0842, 1993, p. 24–42.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Blumberg, L.M. Relations between pneumatic parameters of ideal gas in a column with uniform permeability. Chromatographia 41, 15–22 (1995). https://doi.org/10.1007/BF02687994
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02687994